Perpendicular Lines Worksheet

**Page 1**

1.

What is the slope of a line perpendicular to 2$x$ + 3$y$ + 9 = 0?

a. | $\frac{3}{2}$ | ||

b. | - $\frac{3}{2}$ | ||

c. | $\frac{2}{3}$ | ||

d. | - $\frac{2}{3}$ |

[Simplify.]

Slope of the line is -

[Compare with

Slope of required line × Slope of 2

[Product of slopes of perpendicular lines is - 1.]

Slope of required line × -

[Substitute.]

Slope of required line =

[Simplify.]

Correct answer : (1)

2.

What can you say about the lines 3$x$ + 2$y$ + 5 = 0 and 2$x$ - 3$y$ + 7 = 0?

a. | parallel | ||

b. | perpendicular | ||

c. | collinear | ||

d. | at 60 ^{o} with respect to each other |

[Slope =

Slope of 2

[Slope =

Product of slopes = -

The given lines are perpendicular .

[If product of slopes is -1, then the lines are perpendicular.]

Correct answer : (2)

3.

If the line through ($x$, 3) and (4, 9) is perpendicular to the line through (- 1, 4) and (3, 6), then what is the value of $x$?

a. | 10 | ||

b. | 16 | ||

c. | 4 | ||

d. | 7 |

Slope of

[Slope formula is

Slope of

[Slope formula.]

[Product of slopes of perpendicular lines is - 1.]

[Simplify.]

Correct answer : (4)

4.

What is the product of the slopes of the lines $x$ = 7 and $y$ = 7 ?

a. | not defined | ||

b. | 49 | ||

c. | -1 |

Slope of a vertical line is not defined .

So, the product of the slopes of

Correct answer : (1)

5.

Identify the correct statement.

I. The coordinate axes are perpendicular to each other

II. The coordinate axes are vertical

III. The coordinate axes are horizontal.

IV. The coordinate axes are parallel to each other.

I. The coordinate axes are perpendicular to each other

II. The coordinate axes are vertical

III. The coordinate axes are horizontal.

IV. The coordinate axes are parallel to each other.

a. | II | ||

b. | I | ||

c. | III | ||

d. | IV |

The coordinate plane is formed by two number lines, called the axes, intersecting at right angles.

The

The

The two axes meet at the origin.

Hence the coordinate axes are perpendicular to each other.

Correct answer : (2)

6.

What is the slope of the line perpendicular to 2$x$ + 3$y$ + 6 = 0?

a. | $\frac{-2}{3}$ | ||

b. | $\frac{2}{3}$ | ||

c. | $\frac{3}{2}$ | ||

d. | $\frac{-3}{2}$ |

[Slope =

Slope of required line × Slope of 2

[Product of slopes of perpendicular lines = -1.]

Slope of required line =

[Substitute and simplify.]

Correct answer : (3)

7.

a. | at an angle of 45 ^{o} with respect to each other | ||

b. | perpendicular | ||

c. | parallel | ||

d. | same |

Slope of

[Step 1.]

Slope of

[Step 1.]

Product of slopes of

[Step 2 and Step 3.]

Lines

[If the product of the slopes is - 1, then the lines are perpendicular.]

Correct answer : (2)

8.

What is the slope of a line perpendicular to $y$ = 4 ?

a. | not defined | ||

b. | 4 | ||

c. | -1 |

Slope of required line is not defined .

[Slope of vertical lines is not defined.]

Correct answer : (2)

9.

Which of the following is not perpendicular to $y$ = 2$x$ + 6 ?

a. | 6$y$ + 3$x$ + 10 = 0 | ||

b. | 2$y$ = $x$ + 5 | ||

c. | 4$y$ + 2$x$ + 7 = 0 | ||

d. | 8$x$ + 4$y$ + 8 = 0 |

[Compare with

2

[Rearrange.]

Slope of 2

[Compare with

Product of slopes of

[Step 1 and Step 3.]

All other lines given except 2

[Slope of each is -

Correct answer : (2)

10.

Find the inclination of a line perpendicular to $y$ = $x$ - 3 .

a. | 45 ^{o} | ||

b. | 60 ^{o} | ||

c. | 135 ^{o} | ||

d. | 90 ^{o} |

Slope of

[Compare with

Slope of the required line is - 1.

[Product of slopes of perpendicular lines is - 1.]

[Slope =

θ = 135

[

The inclination of a line perpendicular to

Correct answer : (3)